Traceable In Situ Microwave Power Measurement at the Cryogenic Device Plane in a Dilution Refrigerator

Accurately measuring the microwave power delivered to a device under test (DUT) inside a dilution refrigerator is notoriously difficult due to complex factors like distributed attenuation, impedance mismatches, and temperature-dependent component behavior. This paper addresses the need for an SI-traceable method to calibrate microwave power directly at the millikelvin device plane, bypassing the inaccuracies inherent in room-temperature estimates.

The researchers developed a custom Variable Temperature Stage (VTS) that acts as a cryogenic thermal-transfer element. The VTS is thermally coupled to the refrigerator's cold finger and is equipped with a DC heater, a thermometer, and a 20 dB pass-through attenuator. The method relies on AC/DC substitution: the VTS is alternately heated by a known DC electrical power and the microwave power being measured. By fitting the resulting thermal transients and comparing steady-state temperatures, the absorbed microwave power is inferred. To ensure the result refers to the DUT reference plane, the authors use a switch-assisted Short-Open-Load-Reciprocal (SOLR) calibration to account for the scattering parameters of the cryogenic components.

The system was successfully demonstrated in a dilution refrigerator at 4 GHz. The researchers achieved a relative standard uncertainty of approximately 2% at -43.9 dBm, which increased to about 40% at the lower power level of -57.6 dBm. The uncertainty budget is dominated by slow fluctuations in the parasitic background power and the drift of the cold finger temperature. This architecture provides a robust, practical framework for traceable power calibration in quantum-device experiments.

As superconducting quantum circuits become more complex, precise control over the electromagnetic environment is critical for minimizing decoherence and unwanted effects like AC Stark shifts. By providing a method to calibrate power directly at the millikelvin stage, this work reduces reliance on room-temperature assumptions and improves the reliability of quantum device characterization.